The tamed Milstein method for commutative stochastic differential equations with non-globally Lipschitz continuous coefficients

  title={The tamed Milstein method for commutative stochastic differential equations with non-globally Lipschitz continuous coefficients},
  author={Xiaojie Wang and Siqing Gan},
  journal={Journal of Difference Equations and Applications},
  pages={466 - 490}
  • Xiaojie Wang, S. Gan
  • Published 3 February 2011
  • Mathematics
  • Journal of Difference Equations and Applications
For stochastic differential equations (SDEs) with a superlinearly growing and globally one-sided Lipschitz continuous drift coefficient, the classical explicit Euler scheme fails to converge strongly to the exact solution. Recently, an explicit strongly convergent numerical scheme, called the tamed Euler method, has been proposed in [8] for such SDEs. Motivated by their work, we here introduce a tamed version of the Milstein scheme for SDEs with commutative noise. The proposed method is also… 
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